High dimensional graphical models have become increasingly popular, over the last several decades, for understanding independence and conditional independence relationships
among components of high dimensional random vectors. The challenges posed by the estimation and statistical analysis of a graphical model with many more nodes than the
the number of observations led to renewed interest in these models, and to a very large body of literature, including [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, to give only an incomplete list. However, in practice, when the dimension is very large and the sample size is small, the dependency among variables may become very weak, if it exists, and difficult to detect without auxiliary information. Moreover, when the number of variables is in the tens of thousands, it is difficult to form an opinion of their overall dependency structure, even at the visual level, from a graph estimated via a graphical model.
